To prepare lime syrup, combine lime juice and sugar in a small saucepan and place over medium heat. Heat until sugar is dissolved, 2 to 3 minutes. Pour into a small bowl, cover and refrigerate until completely cool.

Before making ice cream base, make sure that all ingredients are well chilled. Slice avocados in half, remove pits, and scoop out the flesh into a blender or food processor. Add sugar, yogurt, milk, cream, and salt. Blend until smooth. Add lime syrup and pulse to combine (mixture will be thick). Pour into an ice cream maker immediately* and churn according to the manufacturer’s instructions. Transfer to a freezer-safe container and freeze until firm, at least 4 hours.

*Note: Immediate freezing is necessary to prevent browning. If you don't want to make the ice cream immediately, place the unchurned ice cream base directly into the freezer. When ready to use, thaw in the refrigerator and then follow directions for churning.